[Paper Review] Modelling the host galaxies of binary compact object mergers with observational scaling relations

Filippo Santoliquido, Michela Mapelli+2 more|arXiv (Cornell University)|May 10, 2022

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy162 references36 citations

TL;DR

This paper introduces galaxyRate, a fast numerical code that models the host galaxies of binary compact object (BCO) mergers using observational scaling relations—such as the stellar mass function, star formation rate distribution, and metallicity relations (MZR and FMR). It distinguishes between formation galaxies (FGs) and host galaxies (HGs), showing that BBH and BHNS mergers form in low-mass, metal-poor galaxies but merge in massive, metal-rich hosts, while BNS mergers form and merge in massive galaxies. The model predicts that 5–10% of BNS, 15–25% of BHNS, and 15–35% of BBH mergers occur in passive galaxies locally.

ABSTRACT

The merger rate density evolution of binary compact objects and the properties of their host galaxies carry crucial information to understand the sources of gravitational waves. Here, we present galaxyRate, a new code that estimates the merger rate density of binary compact objects and the properties of their host galaxies, based on observational scaling relations. We generate our synthetic galaxies according to the galaxy stellar mass function. We estimate the metallicity according to both the mass-metallicity relation (MZR) and the fundamental metallicity relation (FMR). Also, we take into account galaxy-galaxy mergers and the evolution of the galaxy properties from the formation to the merger of the binary compact object. We find that the merger rate density changes dramatically depending on the choice of the star-forming galaxy main sequence, especially in the case of binary black holes (BBHs) and black hole neutron star systems (BHNSs). The slope of the merger rate density of BBHs and BHNSs is steeper if we assume the MZR with respect to the FMR, because the latter predicts a shallower decrease of metallicity with redshift. In contrast, binary neutron stars (BNSs) are only mildly affected by both the galaxy main sequence and metallicity relation. Overall, BBHs and BHNSs tend to form in low-mass metal-poor galaxies and merge in high-mass metal-rich galaxies, while BNSs form and merge in massive galaxies. We predict that passive galaxies host at least ~5-10%, ~15-25%, and ~15-35% of all BNS, BHNS and BBH mergers in the local Universe.

Motivation & Objective

• To model the cosmic merger rate density of binary compact objects (BCOs) and characterize their host galaxy (HG) properties using observational scaling relations.
• To address the gap in understanding how host galaxy properties—especially mass, star formation rate (SFR), and metallicity—evolve from BCO formation to merger.
• To quantify the impact of different metallicity relations (MZR vs. FMR) and star-forming main sequence assumptions on merger rate density and host galaxy demographics.
• To assess the contribution of passive galaxies to hosting BCO mergers, particularly in the local Universe.
• To provide a computationally efficient alternative to cosmological simulations for probing BCO merger parameter space.

Proposed method

• galaxyRate generates synthetic galaxies based on the observed galaxy stellar mass function and SFR distribution across cosmic time.
• It estimates metallicity using both the mass-metallicity relation (MZR) and the fundamental metallicity relation (FMR), with redshift-dependent evolution.
• A novel conditional probability algorithm differentiates between the formation galaxy (FG) and the host galaxy (HG), accounting for galaxy mergers and evolution over the BCO delay time.
• The code uses merger trees from the EAGLE cosmological simulation to model galaxy mass and SFR evolution, enabling realistic tracking of FG-to-HG transitions.
• It incorporates delay times from up-to-date binary population synthesis simulations (mobse), with sensitivity to common-envelope efficiency (α) and metallicity.
• The model is flexible and can accept external catalogs from phenomenological BCO merger models, enabling broad parameter space exploration.

Experimental results

Research questions

• RQ1 How does the choice of star-forming main sequence affect the predicted merger rate density of BBHs, BHNSs, and BNSs?
• RQ2 To what extent do the MZR and FMR yield different predictions for the host galaxy properties of BCO mergers?
• RQ3 How does the delay time distribution influence the mass and SFR evolution of host galaxies compared to formation galaxies?
• RQ4 What fraction of BCO mergers occur in passive galaxies, and how does this depend on the definition of 'passive'?
• RQ5 Why is the predicted BBH merger rate density higher than the LVK GWTC-3 range, and what role do formation channel assumptions play?

Key findings

• The merger rate density of BBHs and BHNSs is steeper when using the MZR compared to the FMR, due to the FMR predicting a shallower decline in metallicity with redshift.
• BBH and BHNS mergers form in low-mass, metal-poor galaxies but merge in high-mass, metal-rich galaxies, while BNS mergers form and merge in massive galaxies with similar FG and HG properties.
• The model predicts that 5–10% of BNS, 15–25% of BHNS, and 15–35% of BBH mergers in the local Universe occur in passive galaxies, depending on the passive galaxy definition.
• The discrepancy between predicted and observed BBH merger rate densities may stem from overestimation in binary evolution models or the neglect of dynamical formation channels.
• The delay time distribution, influenced by common-envelope efficiency (α), affects HG mass: longer delays (α = 5) lead to more massive HGS due to galaxy merging, while shorter delays (α = 1) result in more mergers in low-mass galaxies.
• The BNS merger rate per galaxy correlates strongly with host galaxy stellar mass, while this correlation is weaker for BBHs and BHNSs, especially under the FMR.